Recently, various mechanical and physiological simulations are being performed by CAD (Computer Aided Design), biological function analysis, surgery training systems and the like in mechanical engineering, fields related to materials and substances, and fields of medicine and medical services (see Non-patent Document 1, Non-patent Document 2 and Non-patent Document 3). On such occasions, the data mainly used for the simulations is large-scale three-dimensional data, and a variety of visualization approaches, including volume rendering (see Non-patent Document 4 and Non-patent Document 5), are used for visualizing analysis results.
In the case of analyzing the mechanical characteristics of a mechanical part, an elastic material, a human organ or the like, a three-dimensional mesh is prepared from a set of tomograms obtained by CT, MRI or the like after performing region extraction, surface generation and the like as pre-processing. Displacement of the constructed mesh is obtained using a mechanical calculation solver, and the analysis result is visualized by surface polygon rendering or cell-projection (see Non-patent Document 6 and Non-patent Document 7).
There is also an approach that carries out voxelization once again from the mesh form after a simulation and performs volume rendering (see Non-patent Document 8 and Non-patent Document 9). During the voxelization, volume texture after deformation is newly created each time, while referring to the voxel grey value of the original image.    Non-patent Document 1 I. Fujishiro, L. Chen, Y. Takeshima, H. Nakamura and Y. Suzuki, “Parallel Visuzalization of Gigabyte Datasets in GeoFEM”, Concurrency and Computation: Practice and Experience, Vol. 14, No. 6-7, pp. 521-530, 2002    Non-patent Document 2 B. Wunsche, “The Visualization and Measurement of Left Ventricular Deformation”, Proc. the First Asia-Pacific bioinformatics conference on Bioinformatics, pp. 119-128, 2003.    Non-patent Document 3 B. Pflesser, U. Tiede, K. H. Hohne and R. R. Leuwer, “Volume Based Planning and Rehearsal of Surgical Intervention”, Proc. Computer Assisted Radiology and Surgery (CARS), pp. 607-612, 2000    Non-patent Document 4 R. A. Drebin, L. Carpenter and P. Hanrahan, “Volume Rendering”, Computer Graphics (Proc. ACM SIGGRAPH), Vol. 22, No. 4, pp. 65-74, 1988.    Non-patent Document 5 F. Dachille, K. Kreeger, B. Chen, I. Bitter and A. Kaufman, “High-quality Volume Rendering Using Texture Mapping Hardware”, Proc. The ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware, p. 69, 1998.    Non-patent Document 6 M. Weiler, M. Kraus, M. Merz and T. Ertl, “Hardware-Based Ray Casting for Tetrahedral Meshes”, Proc. IEEE Visualization, pp. 333-340, 2003.    Non-patent Document 7 M. Weiler, M. Kraus and T. Ertl, “Hardware-Based View-Independent Cell Projection”, Proc. the IEEE Symposium on Volume Visualization and Graphics, pp. 13-22, 2002.    Non-patent Document 8 A. E. Kaufman, S. W. Wang, “Volume Sampled Voxelization of Geometric Primitives”, Proc. IEEE Visualization, pp. 78-84, 1993.    Non-patent Document 9 J. Huang, R. Yagel, V. Filippov and Y Kurzion “An Accurate Method for Voxelizing Polygon Meshes”, ACM Symposium on Volume Visualization, pp. 119-126, 1998.